Knots Unravelled

Knots Unravelled is a guide to the fascinating world of knots, from the familiar realm of knotted string to the less familiar branch of mathematics known as knot theory.

Are two given knots the same or different?

How many knots are there?

Can knots be classified?

Questions like this are easily asked, but finding answers requires more effort. Mathematical ideas help to put the study of knots on a firm footing, and also either answer such questions, or explain why an answer cannot be found. The core chapters of Knots Unravelled lead the reader through this mathematics, from the basics to the frontiers of current work in knot theory.

Between the main chapters, the `interludes' reveal some of the rich variety of ways in which knots appear throughout human culture, drawing attention to related mathematics and making connections with other material in the book.

Progress to Advanced Mathematics

Written by a team of highly experienced Mathematics teachers, this book provides carefully selected materials to aid progress towards AS Level, A Level, the IB and other advanced Mathematics examinations.

Students will find this book helps to build their confidence by ensuring they have a good grounding in basic topics before embarking on advanced material.

In particular, the book will help to develop the fluency in algebra necessary for success in advanced work.

Progress to Advanced Mathematics is designed for use either before starting sixth form studies or as introductory exercises throughout the teaching of the course, and will help students to:

practise the essential skills needed for AS and A Level;

consolidate material from GCSE;

develop proficiency in algebra;

gain a firm understanding of the basics of graphs, coordinate geometry and trigonometry.

Geometric Origami

How do you fold regular polygons?

Can more be achieved by folding paper than by traditional ‘ruler and compass’ constructions?

Geometric Origami
reveals some of the rich mathematics inherent in paper folding, and will help origamists, mathematicians and the interested general reader appreciate the value of studying the geometrical properties of folding a square of paper.

Part I of the book covers the mathematical theory of origami constructions.

Part II includes step-by-step folding instructions for fifteen regular polygons, from the equilateral triangle to the 19-gon.

Written by the mathematician and origamist Robert Geretschläger, Geometric Origami will appeal to:

Progress to Higher Mathematics

Written by a team of highly experienced Mathematics teachers, Progress to Higher Mathematics provides carefully selected materials which will aid progression towards the Higher Mathematics examination offered by the Scottish Qualifications Authority.

Designed for use either as a precursor to the Higher syllabus or as introductory exercises throughout the teaching of the course, Progress to Higher Mathematics will help students to:

build on previous knowledge and skills gained at National 5, Standard Grade or Intermediate 2

consolidate the essential skills necessary for Higher Mathematics

enhance algebraic expertise

utilize graphicacy as a means of improving mathematical understanding

develop the geometrical ideas needed for a thorough understanding of analytical geometry